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Primal cutting plane algorithms revisited

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  • Adam N. Letchford
  • Andrea Lodi

Abstract

Dual fractional cutting plane algorithms, in which cutting planes are used to iteratively tighten a linear relaxation of an integer program, are well-known and form the basis of the highly successful branch-and-cut method. It is rather less well-known that various primal cutting plane algorithms were developed in the 1960s, for example by Young. In a primal algorithm, the main role of the cutting planes is to enable a feasible solution to the original problem to be improved. Research on these algorithms has been almost non-existent. In this paper we argue for a re-examination of these primal methods. We describe a new primal algorithm for pure 0-1 problems based on strong valid inequalities and give some encouraging computational results. Possible extensions to the case of general mixed-integer programs are also discussed. Copyright Springer-Verlag Berlin Heidelberg 2002

Suggested Citation

  • Adam N. Letchford & Andrea Lodi, 2002. "Primal cutting plane algorithms revisited," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(1), pages 67-81, August.
    • Handle: RePEc:spr:mathme:v:56:y:2002:i:1:p:67-81
    DOI: 10.1007/s001860200200
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    Cited by:

    1. Santanu S. Dey & Jean-Philippe Richard, 2009. "Linear-Programming-Based Lifting and Its Application to Primal Cutting-Plane Algorithms," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 137-150, February.
    2. Abdelouahab Zaghrouti & Issmail El Hallaoui & François Soumis, 2020. "Improving set partitioning problem solutions by zooming around an improving direction," Annals of Operations Research, Springer, vol. 284(2), pages 645-671, January.

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